Sergei Eisenstein in Physics

Impressed? Come to me!

In reality, the second photo was taken first. This is how
I can make a story by re-arranging photos.

Sergei Eisenstein (1898-1948) was a Soviet-era film maker. What does
he have to do with physics? To Russians, he is known as the producer
of the "The Battleship Potomkin." In the rest of the world, he was
the producer of the first two volumes of the "Ivan the Terrible."

We would normally expect that someone writes a movie story first.
Then actors perform, and a cameraman shoots. Eisenstein had a different
idea. Shoot the camera first, and then compose the story using
those pictures. This is the reason why Ivan the Terrible appears as
two completely different characters in the two volumes.
What does this have to do with me? Webpages!

Since 1959, I have been taking many photos. They were not too useful.
However, since 2001, I started making webpages. To make a webpage,
we have to choose a set of photos, place them in proper order, and
then write in stories. This is how I make my webpages. I do not know
how else one can produce the pages. This is precisely what I learned
from Eisenstein.

Let us see how Eisensteinism works. I took these two photos in 2002.
The second photo was taken first at a different place. But the
combination of the two makes a perfect story. The web stories do
not have have to tell lies. I enjoy more when I tell true stories.
Here are some webpages constructed from my old photos.

If you think my webpages are trying to tell you something, it is because
of the lesson I learned from Sergei Eisenstein.

I have been making webpages since 2000 AD. I had to construct stories
based on the photos I have taken in the past. I had to combine those
photos in a judicious order. I then realized I was practicing
Eisensteinism.

If anyone has a distinctive new idea, it is usually a product of his/her
childhood environment. For instance, Kant's philosophy was based on the
geographical condition of Koenigsberg (now Kaliningrad) where Kant spent
80 years of his entire life. Here is
my webpage dedicated to this subject.

Eisenstein could not be an exception. In order to find out what environment
he had during his early years, I went in June of 2010 to Riga (Latvia)
where he was born and raised. While talking with Latvians there, I learned
that his father came from Saint Petersburg and became a very prominent
architect. There are still some beautiful buildings designed by him. Great!
I went to those buildings and could see immediately how Eisenstein became so
creative.

To make a long story short, let us look at one of those buildings designed by
his father.

This architect of course had his reasons to bring many things from
different places. However, his design forces us to think beyond what
we see. The architect was Sergei Eisenstein's father.

Very definitely, Sergei was strongly influenced by his father. He looks
at the photos he has taken, and then thinks carefully about what idea he
could produce from those photos. This is what Eisenstein's creativity
is all about.

Let us translate this into your issue. You have published many papers in
the past. Look at them again, and try to construct a new idea from them.

Eisensteinism does not end here. Humans from their beginning had a
habit of looking at the stars during the night and made attempts to make
sense out of them. We still carry this habit of watching the sky. We
do cosmology, black holes, dark matter, gravitational waves, and many
more to come.

By 1500 AD, humans observed that some of those heavenly objects follow
elliptic or hyperbolic trajectories. Isaac Newton then wrote down a
second-order differential equation for both.

In quantum mechanics, this translates into running waves and standing waves.
Here again, Erwin Schroedinger's second-order differential equation
takes care of this problem. The question then is how to deal with this
problem in Einstein's Lorentz-covariant world.
Click here for further discussion.

As for the geometry of ellipse and hyperbola, ancient Greeks came up
with the using a circular cone. This cone contains both ellipse and hyperbola.

When I was 15 years old, I learned that the equation

A x 2 + B y2 = Constant

can produce both ellipse and hyperbola, and is as good at the circular cone
used by those Greeks.

If this equation looks too childish to you, you can
consider a two-by-two unimodular matrix with real elements. It has three
independent parameters, but it can be brought to an equi-diagonal form by
a rotation. Then the matrix has two independent parameters and takes one of
the following three forms.

The first matrix is a squeezed rotation matrix, and is therefore for an
elliptic orbit. The second matrix is for a hyperbolic orbit. The third
is for a linear orbit. If we construct a four-by-four matrix, it will
be quadratic in the parameter, and thus represent a parabolic orbit.

The question then is whether these three matrices can be combined into
one analytic matrix. The answer is Yes. We can use the mathematical
technique called the Bargmann decomposition to combine all three of
the above matrices into one expression, given as

Indeed, this matrix is analytic in both \lambda and \theta
variables in the entire applicable region. The boundary
between ellipse and hyperbola is given by the diagonal
line.

What I said above is strictly about mathematical aspect
of two-by-two matrices. However, it is applicable to
at least two important branches of modern physics.

In 1939, Eugene Wigner published his paper on the
little groups which dictate the internal space-time
symmetries of particles in the Lorentz-covariant
world. The three equi-diagonal matrices given above
serve as the basis for Wigner's little group.

Wigner always wanted to translate his 1939 paper into
the language of two-by-two matrices. It appears that
Wigner's little groups emerge from this simple
mathematical property of the two-by-two matrix.

There are many other branches of physics I am not competent
to speak about. However, solutions are possible only if the
problems are brought into the form of harmonic oscillators
or/and two-by-two matrices, since otherwise they cannot be
solved.

I made the above conclusion by looking at the many of my past
papers, as Sergei Eisenstein constructed new stories based
on the photos he took. Many people complain that my papers
contain only two-by-two matrices, ellipses, and hyperbolas. But
they cannot complain about what I said above.

So far, we have been treating ellipse and hyperbola as different curves.
I am not satisfied with this observation. I am interested in whether the
hyperbola and ellipse are the same thing. For this purpose, let us write
another baby formula, namely

x2 - y2 = (x + y) (x - y) .

If (x2 - y2) remains constant as in the case of
hyperbola,
(x - y) should become smaller as (x + y) becomes large. This means that
there is an ellipse for each point on the hyperbolic trajectory.

In 1962, I had an audience with Paul A. M. Dirac. He told me to study
the contents of Lorentz covariance. Since Dirac told me so, I had to
read his papers. His papers are like poems, but they do not contain figures.
Thus, I decided to translate his poems into
one picture. On this project, I have been working with Marilyn
Noz since 1973. You may
click here for our latest
paper on this subject.

I already talked too much about myself. I could talk more, but I should stop
here. I took many photos while in Riga. I have placed some of them on this
webpage, and will place more when I have time. Let us look at those photos.

Photos from Riga (June 2010)

Panoramic View of Riga.
room. Riga is an old city. I took this photo from my hotel room on the
15th floor of the Raddison Blue hotel.

Statue of Liberty. Latvia
is a small country, and has been invaded and liberated a number of times
throughout her history. Latvians had reasons to celebrate whenever they became
liberated. There are a number of statues like this in Riga.

Major Transportation Hub.
Riga grew as a major harbor for the Baltic Sea. Even these days, giant
ocean liners can come to the city through the Daugava channel. This river is
like New York's

airBaltic has its
hub in Riga. I was talking with these two airBaltic ladies in the
lobby of the Radisson Blu Hotel. They said their ariline is affiliated with
the SAS Scandinavian Airlines.

Briefed about Riga. While
waiting for a fight from Warsaw to Riga, I was talking with this Latvian
economist. She gave me a brief history lesson about her country.

Latvian Professionals
I met in Cannes, France. They came here from Riga for vacation (June 2006).
They have been to the United States, and seem to have a bright future in their
country.

Another Latvian Professional
I met at Warsaw's Frederic Chopin Airport in 2008. She claimed that Latvian
women are most beautiful in the world. I then asked her whether I can have
a photo with her, and she cheerfully agreed. At that time, I was going to
Vilnius (Lithuania). She told me I should visit her country also, and I did in 2010.

American Lady from Chicago. She was
born and raised in Riga, but she now lives in Chicago. I was talking with this
American lady on the airport bus. She was going back to her
home after seeing her relatives in Riga. She was very happy.

Riga's Opera House. Like
all European cities, the opera house is at the center of the city. There is
a beautiful city park in front of this center of musical art.

Russian Orthodox Church.
built during the 19th century while Riga was under influence of the Romanov Empire.
Russians left after their 1917 revolution, but Soviets came back after World War II.
Russians constitute about 49 percent of the Latvian population. Many of those
Russians became naturalized to Latvian citizens, but there are still many who are
proud to be Russians.

This Russian lady owns her
amber shop in Riga. She is very proud of her Russian heritage, and she speaks only
Russian and refuses to speak any other language. I cannot speak Russian too well,
but managed to communicate with her. She was very happy with me because I bought
some items from her.

Young Russian Professor
very proud to be a Russian while living in Riga. I met her at Washington's
Dulles International Airport in 2004.

Ford Cars for
Riga taxi cabs. They were assembled in the Russian Baltic city of
Kaliningrad. Other popular cars are also
assembled there for Russian consumers, but Ford seems to be something to Latvians.
Do you know where Kaliningrad is?
Click here.

Pizza House. Italians
Invented pizza, but pizza houses are popular worldwide because there are
many of them in the United States.

Sushi is traditional Japanese
food, but it is becoming very popular in the United States. Latvians seem to
follow this American trend.

Mikhail Eisenstein was
a very prominent architect in Riga. Most of the traditional buildings were
influenced by him. There are still six buildings originally designed by him.
Let us see some of those buildings.

Wooden Buildings. Vikings developed
the technology of putting wooden pieces together to build ships. The result had to
be water-tight. Latvians extended this technology to build wind-tight houses. There are
many wooden buildings like this in Riga.